You are on a game show and there are three doors. The presenter tells you that behind one of doors there is a car and behind the other two are goats, if you pick the car you win it. After you have picked a door the presenter opens a different door with a goat behind it, he then gives you the chance to change what door you open, what should you do?

Solution

You want to change your decision. The initial decision has a 1 in 3 shot of being correct. Changing to the alternate door has a 2/3 chance of being correct. Think of it this way, if your initial pick is not the car (which has a 2/3 probability) then it must be that the alternate unopened door IS the car.